Analysis Seminar

5/23/2006

Benjamin Schlein

Harvard University

Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates

In this talk I am going to report on a recent result obtained in collaboration with L. Erdoes and H.-T. Yau. We consider a system of N interacting bosons in the Gross-Pitaevskii limit, where N tends to infinity and the scattering length of the pair potential is of the order 1/N.  In this limit we prove that the macroscopic dynamics of the system is correctly described by the time-dependent Gross-Pitaevskii equation, a cubic nonlinear Schroedinger equation for the wave function of the condensate.